In co-pending and commonly assigned PCT Application No. PCT/IL/01/00335, published as WO 01/77629, U.S. Pat. No. 6,819,435, and PCT Application No. PCT/IL02/00833, published as WO 03/062743, all of which are incorporated herein by reference, each in its entirety, there are described methodologies and systems for wavefront analysis as well as for surface mapping, phase change analysis, spectral analysis, object inspection, stored data retrieval, three-dimensional imaging and other suitable applications utilizing wavefront analysis.
Some principles of these methods are described in FIGS. 1 and 2. FIG. 1 shows a simplified partially schematic, partially pictorial illustration of wavefront analysis functionality. The functionality of FIG. 1 can be summarized as including the following sub functionalities:    I. Obtaining a plurality of differently phase changed transformed wavefronts corresponding to a wavefront being analyzed, which has an amplitude and a phase;    II. Obtaining a plurality of intensity maps of the plurality of phase changed transformed wavefronts; and    III. Employing the plurality of intensity maps to obtain an output indicating at least one and possibly both of the phase and the amplitude of the wavefront being analyzed.As seen in FIG. 1, the first sub-functionality, designated “A” may be realized by the following functionalities: A wavefront, which may be represented by a plurality of point sources of light, is generally designated by reference numeral 100. Wavefront 100 has a phase characteristic which is typically spatially non-uniform, shown as a solid line and indicated generally by reference numeral 102. Wavefront 100 also has an amplitude characteristic which is also typically spatially non-uniform, shown as a dashed line and indicated generally by reference numeral 103. Such a wavefront may be obtained in a conventional manner by receiving light from any object, such as by reading an optical disk, for example a DVD or compact disk 104.
The method enables the measurement of the phase characteristic, such as that indicated by reference numeral 102, and the amplitude characteristic, such as that indicated by reference numeral 103 in an enhanced manner. It should be noted that since, by definition of phase, a phase characteristic is a relative characteristic, the term refers to the relative phase map or to the phase differences between any two points in the wavefront. In general, throughout this application, and where claimed, all references relating to measurements or calculations of “phase”, or similar recitations such as phase maps, are understood to mean such measurements or calculations of a phase shift, or of a phase difference, or of a relative phase referred to the particular phase context under discussion in that location.
A transform, indicated symbolically by reference numeral 106, is applied to the wavefront being analyzed 100, thereby to obtain a transformed wavefront, symbolically indicated by reference numeral 108. A plurality of different phase changes, preferably spatial phase changes, represented by optical path delays 110, 112 and 114 are applied to the transformed wavefront 108, thereby to obtain a plurality of differently phase changed transformed wavefronts, represented by reference numerals 120, 122 and 124 respectively. It is appreciated that the illustrated difference between the individual ones of the plurality of differently phase changed transformed wavefronts is that portions of the transformed wavefront are delayed differently relative to the remainder thereof.
The second sub-functionality, designated “B”, is realized by applying a transform, preferably a Fourier transform, to the plurality of differently phase changed transformed wavefronts. Finally, functionality B requires detection of the intensity characteristics of plurality of differently phase changed transformed wavefronts. The outputs of such detection are the intensity maps, examples of which are designated by reference numerals 130, 132 and 134.
The third sub-functionality, designated “C” may be realized by the following functionalities: expressing, such as by employing a computer 136, the plurality of intensity maps, such as maps 130, 132 and 134, as at least one mathematical function of phase and amplitude of the wavefront being analyzed and of the plurality of different phase changes, wherein at least one and possibly both of the phase and the amplitude are unknown and the plurality of different phase changes, typically represented by optical path delays 110, 112 and 114 to the transformed wavefront 108, are known; and employing, such as by means of the computer 136, the at least one mathematical function to obtain an indication of at least one and possibly both of the phase and the amplitude of the wavefront being analyzed, herein represented by the phase function designated by reference numeral 138 and the amplitude function designated by reference numeral 139, which, as can be seen, respectively represent the phase characteristics 102 and the amplitude characteristics 103 of the wavefront 100. Wavefront 100 may represent the information contained or the height map of the measured object, such as compact disk or DVD 104 in this example.
An example of a simplified partially schematic, partially block diagram illustration of a wavefront analysis system suitable for carrying out the functionality of FIG. 1 is depicted in FIG. 2. As seen in FIG. 2, a wavefront, here designated by reference numeral 150 is focused, as by a lens 152, onto a phase manipulator 154, which is preferably located at the focal plane of lens 152. The phase manipulator 154 generates phase changes, and may be, for example, a spatial light modulator or a series of different transparent, spatially non-uniform objects. A second lens 156 is arranged so as to image wavefront 150 onto a detector 158, such as a CCD detector. Preferably the second lens 156 is arranged such that the detector 158 lies in its focal plane. The output of detector 158 is preferably supplied to data storage and processing circuitry 160, which preferably carries out functionality “C” described herein above with reference to FIG. 1.
A simplified partially schematic, partially pictorial illustration of a system for surface mapping employing the functionality and structure of FIG. 1, is depicted in FIG. 3. As seen in FIG. 3, a beam of radiation, such as light or acoustic energy, is supplied from a radiation source 200 optionally via a beam expander 202, onto a beam splitter 204, which reflects at least part of the radiation onto a surface 206 to be inspected. The radiation reflected from the inspected surface 206, is a surface mapping wavefront, which has an amplitude and a phase, and which contains information about the surface 206. At least part of the radiation incident on surface 206 is reflected from the surface 206 and transmitted via the beam splitter 204 and focused via a focusing lens 208 onto a phase manipulator 210, which is preferably located at the image plane of radiation source 200. The phase manipulator 210 may be, for example, a spatial light modulator or a series of different transparent, spatially non-uniform objects. A second lens 212 is arranged so as to image surface 206 onto a detector 214, such as a CCD detector. Preferably the second lens 212 is arranged such that the detector 214 lies in its focal plane. The output of detector 214, an example of which is a set of intensity maps designated by reference numeral 215, is preferably supplied to data storage and processing circuitry 216, which preferably carries out functionality “C” described hereinabove with reference to FIG. 1, providing an output indicating at least one and possibly both of the phase and the amplitude of the surface mapping wavefront. This output is preferably further processed to obtain information about the surface 206, such as geometrical variations and reflectivity of the surface. The phase manipulator 210 is described as applying a plurality of different spatial phase changes to the radiation wavefront reflected from surface 206 and Fourier transformed by lens 208. Application of the plurality of different spatial phase changes provides a plurality of differently phase changed transformed wavefronts which may be subsequently detected by detector 214.
The general principles of the algorithms and computation methods are depicted in FIG. 4, which depicts a simplified functional block diagram illustration of part of the functionality of FIG. 1. In the exemplary arrangement shown in FIG. 4, the transform applied to the wavefront being analyzed is a Fourier transform, at least three different spatial phase changes are applied to the thus transformed wavefront, and at least three intensity maps are employed to obtain indications of at least one of the phase and the amplitude of the wavefront. As seen in FIG. 4, and designated as sub-functionality “C” hereinabove with reference in FIG. 1, the intensity maps are employed to obtain an output indication of at least one and possibly both of the phase and the amplitude of the wavefront being analyzed.
It is seen in FIG. 4 that the wavefront being analyzed is expressed as a first complex function ƒ(x)=A(x)eiφ(x), where ‘x’ is a general indication of a spatial location. The complex function has an amplitude distribution A(x) and a phase distribution φ(x) identical to the amplitude and phase of the wavefront being analyzed. The first complex function ƒ(x)=A(x)eiφ(x) is indicated by reference numeral 300. Each of the plurality of different spatial phase changes is applied to the transformed wavefront preferably by applying a spatially uniform spatial phase delay having a known value to a given spatial region of the transformed wavefront. As seen in FIG. 4, the spatial function governing these different phase changes is designated by ‘G’ and an example of which, for a phase delay value of θ, is designated by reference numeral 304. Function ‘G’ is a spatial function of the phase change applied in each spatial location of the transformed wavefront. In the specific example designated by reference numeral 304, the spatially uniform spatial phase delay, having a value of θ, is applied to a spatially central region of the transformed wavefront, as indicated by the central part of the function having a value of θ, which is greater than the value of the function elsewhere.
A plurality of expected intensity maps, indicated by spatial functions I1(x), I2(x) and I3(x), are each expressed as a function of the first complex function f(x) and of the spatial function G, as indicated by reference numeral 308. Subsequently, a second complex function S(x), which has an absolute value |S(x)| and a phase α(x), is defined as a convolution of the first complex function f(x) and of a Fourier transform of the spatial function ‘G’. This second complex function, designated by reference numeral 312, is indicated by the equation S(x)=f(x)*=|S(x)|eiα(x), where the symbol ‘*’ indicates convolution and  is the Fourier transform of the function ‘G’. The difference between φ(x), the phase of the wavefront, and α(x), the phase of the second complex function, is indicated by ψ(x), as designated by reference numeral 316.
The expression of each of the expected intensity maps as a function of f(x) and G, as indicated by reference numeral 308, the definition of the absolute value and the phase of S(x), as indicated by reference numeral 312 and the definition of ψ(x), as indicated by reference numeral 316, enables expression of each of the expected intensity maps as a third function of the amplitude of the wavefront A(x), the absolute value of the second complex function |S(x)|, the difference between the phase of the wavefront and the phase of the second complex function ψ(x), and the known phase delay produced by one of the at least three different phase changes which each correspond to one of the at least three intensity maps. This third function is designated by reference numeral 320 and includes three functions, each preferably having the general form In(x)=|A(x)+(eiθn−1)|S(x)|e−iψ(x)|2 where In(x) are the expected intensity maps and n=1, 2 or 3. In the three functions, θ1, θ2 and θ3 are the known values of the uniform spatial phase delays, each applied to a spatial region of the transformed wavefront, thus effecting the plurality of different spatial phase changes which produce the intensity maps I1(x), I2(x) and I3(x), respectively. It is appreciated that preferably the third function at any given spatial location x0 is a function of A, ψ and |S| only at the same spatial location x0. The intensity maps are designated by reference numeral 324.
The third function is solved for each of the specific spatial locations x0, by solving at least three equations, relating to at least three intensity values I1(x0), I2(x0) and I3(x0) at at least three different phase delays θ1, θ2 and θ3, thereby to obtain at least part of three unknowns A(x0), |S(x0)| and ψ(x0). This process is typically repeated for all spatial locations and results in obtaining the amplitude of the wavefront A(x), the absolute value of the second complex function |S(x)| and the difference between the phase of the wavefront and the phase of the second complex function ψ(x), as indicated by reference numeral 328. Thereafter, once A(x), |S(x)| and ψ(x) are known, the equation defining the second complex function, represented by reference numeral 312, is typically solved globally for a substantial number of spatial locations ‘x’ to obtain α(x), the phase of the second complex function, as designated by reference numeral 332. Finally, the phase φ(x) of the wavefront being analyzed is obtained by adding the phase α(x) of the second complex function to the difference ψ(x) between the phase of the wavefront and the phase of the second complex function, as indicated by reference numeral 336.
A wavefront analysis system may include two functionalities—an imaging functionality and an imaged-wavefront analysis functionality, as depicted in FIG. 5 below. The wavefront to be analyzed, 510 is imaged by the imaging functionality 520, to result an imaged-wavefront 530. The imaged wavefront is analyzed by an imaged-wavefront analysis functionality 540, and the resulting information about the wavefront is subsequently processed and stored, by the data storage and processing component 550. It should be noted that imaging functionality 520 and imaged wavefront analysis functionality 540, can be implemented as two sub-functionality of the same joint system, and in such case the imaged wavefront 530, would be generated internally within the same joint system.